A381035 Numbers such that the least significant nonzero digit in their primorial base representation (A049345) is 1.

1, 2, 3, 5, 6, 7, 8, 9, 11, 13, 14, 15, 17, 19, 20, 21, 23, 25, 26, 27, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 51, 53, 55, 56, 57, 59, 61, 62, 63, 65, 66, 67, 68, 69, 71, 73, 74, 75, 77, 79, 80, 81, 83, 85, 86, 87, 89, 91, 92, 93, 95, 96, 97, 98, 99, 101, 103, 104, 105, 107, 109, 110, 111

Offset

1,2

Comments

Numbers k such that A327860(k) is not a multiple of A053669(k), where A327860 is the arithmetic derivative of the primorial base exp-function, and A053669(k) gives the least prime not dividing k.

The asymptotic density of this sequence is 0.70523017... (A064648). - Amiram Eldar, Feb 17 2025

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to primorial base.

Formula

{k such that A276088(k) = 1}.

Example

   n, A049345(n), A276088(n)
  ---------------------------------------------
   4       20       2, thus 4 is not present,
  11      121       1, thus 11 is present,
  14      210       1, thus 14 is present.

Mathematica

q[n_] := Module[{k = n, p = 2, r}, While[{k, r} = QuotientRemainder[k, p]; k > 0 && r == 0, p = NextPrime[p]]; r == 1]; Select[Range[120], q] (* Amiram Eldar, Feb 17 2025 *)

Prog

(PARI)
A276088(n) = { my(e=0, p=2); while(n && !(e=(n%p)), n = n/p; p = nextprime(1+p)); (e); };
is_A381035(n) = (1==A276088(n));

Crossrefs

Complement of A380535 (apart from 0 which is in neither).

Cf. A049345, A064648, A276088, A380534.

Subsequences: A276156, A290249, A381034, A381037, A380527, A392606, A392611.

Sequence in context: A346726 A346724 A346723 * A346722 A007989 A349467

Adjacent sequences: A381032 A381033 A381034 * A381036 A381037 A381038

Keyword

nonn,base,easy

Author

Antti Karttunen, Feb 17 2025

Status

approved